Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology

TL;DR

This paper introduces reduced order modeling techniques to efficiently detect steady bifurcations in incompressible fluid flows, with applications to blood flow asymmetries in cardiology, significantly lowering computational costs.

Contribution

It develops a novel ROM-based approach for identifying steady bifurcations in fluid dynamics, specifically applied to cardiac blood flow analysis.

Findings

ROM reduces computational time for bifurcation detection

Successfully applied to blood flow symmetry breaking

Demonstrates potential for clinical flow analysis

Abstract

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.